King Air pilot conducting training reported a NMAC with unidentified VFR traffic that required a response to a TCAS RA.

Narrative

We were on a ZZZ Tower enroute clearance from ZZZ1 to ZZZ2. After departing ZZZ1 and switching to Departure Control; I asked the controller if we could proceed to enter a holding pattern while enroute to ZZZ2.He said no problem and immediately gave us direct to the ZZZ3 180 degree radial 8 mile fix then direct ZZZ [VOR]. Hold south on the 180 degree radial; right turns and 5 mile legs. We were in busy airspace and climbing. We continued on our current heading and were setting up the 8 mile fix when we received a TA then a RA on the TCAS to climb. At about the same time the controller told us of traffic at 11 o'clock and to climb immediately. We followed the RA and the controller told us to level at 6;000 which we did.We then proceeded inbound to ZZZ [VOR] and entered the hold as described. We then exited the hold after one turn and continued to ZZZ2 uneventfully.With the quick holding instructions from the controller and the time it took to get the fix in the FMS; we were not ready for how fast that traffic occurred. In hindsight we should have asked for a vector to the initial holding fix because with the heavy after departure workload there was no way we could get the initial fix input to the FMS that fast.