A Tower Controller reported a NMAC occurred due to TRACON turning a departing C172 into the path of a subsequent business jet departure without coordination.

Narrative

This ties into safety concern filed earlier in the same day about ZZZ [TRACON]/ZZZ [Tower] LOA (Letter of Agreement) downwind entries; and how it relates into a near mid air collision in this report. Upon arrival to the facility and working the local control position; working on Runway XX; the main runway that benefits us running the agreed upon northwest heading with our departures because numerous aircraft depart that direction. There is only one prop heading without it. Please see previous report for all details. The crew I was relieving stated that ZZZ [TRACON] informed ZZZ [Tower] that we were unable to depart any aircraft on the northwest heading because ZZZ1 an airport 8 miles southwest of ZZZ was on runway XY. Please note that there is nothing agreed to in the LOA that states the Northwest departure are unusable for that configuration. It only states that ZZZ [Tower] has the authority to turn off the downwind arrival acceptance from ZZZ [TRACON]. These were agreed upon at the same time. At most; the configuration would involve having the VFR aircraft fly north a little further before turning Northwest. These are examples of the situations that cause concerns about positions being staffed and willingness to work the aircraft as our traffic quickly increases in numbers.The tower continued to allow downwind entries; more than likely because of the complaints when they are turned off. The tower was; at times dealing with aircraft they could not get out and departed traffic on the only prop heading available; which was southeast. It caused unnecessary delays for departing aircraft. An aircraft decided to taxi back to a hangar from the excessive delays on the ground. These are reported from the controllers working at the time. ZZZ controller continued to work without the LOA assigned heading and allowing VFR downwind entries for several hours.The incident today happened a few hours later after the controllers continued to put prop aircraft out on the southeast heading (90 percent were wanting to go Northwest). The Local Controller cleared Aircraft X for takeoff; departing runway XX on a heading of 140. The Local Controller then cleared Aircraft Y for takeoff heading 170. Once Aircraft Y was off the runway; the ZZZ [TRACON] controller turned Aircraft X to west and the tag displayed the west sector. After the aircraft was turning observed out the window the ZZZ [TRACON] controller asked if Aircraft X could turn west because that was the direction he wanted to go. The local controller told ZZZ [TRACON] that Aircraft Y was departing at that time. After the ZZZ [TRACON] controller hung up; Aircraft Y was observed flying directly at Aircraft X altitude 017 ft. Aircraft X was at 1500 ft. and climbing to 3000 ft. The local controller immediately turned Aircraft Y to a 140 heading. The targets began to merge on the radar; but thankfully Aircraft Y was observed turning in time out the window to miss Aircraft X.I think the overall cause of a situation like this is what I brought up in the previous report; It's easy to make aircraft fly miles out of their way because it takes more effort to work them in the general direction they want to go. It's also easier to put all aircraft into the downwind for tower to sequence. At some point a realization needs to occur. It does make since for the VFR aircraft to go westbound. But this aircraft was flying miles out of their way and turned back into the departure corridor without tower coordination. No turns back into the final without coordination. Its easier to not coordinate and do it anyway. This airport; and this airspace is becoming too busy. The northwest heading was desperately needed to untie the tower's hands and move all this VFR traffic. There needs to be real justification to take it away. ZZZ [Tower] needs more standardization. We need traffic sequenced by the approach control and we need to be able to depart the growing number of aircraft safely. If we were able todepart northwest to begin with; this would not have happened.There should not be a reason the tower cannot launch VFR aircraft on 200 heading off of runway XX. ZZZ [TRACON] was worried about the current procedure that put VFR aircraft on a downwind departure off of runway XX; clear of runway XZ final and then switched on a 300 heading. It's too much for the tower and put aircraft in the general direction of the 19 final; although it still works fine. A 200 heading would be easier for the tower and give ZZZ [TRACON] more options. 8 miles southwest should be no concern for a VFR C172 aircraft on a 200 heading. This would also allow ZZZ [Tower] to depart aircraft without having to place on a downwind and then turn clear of the crossing final and spend more time scanning the runway.