B737 First Officer reported loss of electric speed and stabilizer trim during climbout resulting in a return to the departure airport.

Narrative

We took-off around XA:15 and shortly after departure the master caution light lit up. The speed trim light on the overhead panel illuminated and extinguished. It was our jump seater who noticed the speed trim fail light as it extinguished before we could see it. After that the trim buttons on both Captain and First Officer control wheels where ineffective. Manual trim was still working and the master caution lit up again for the center fuel tanks. The speed trim light illuminated again at some point whilst troubleshooting and complying with the Quick Reference Handbook (QRH) procedures for speed trim fail and loss of electrical stab trim. The Captain was initially flying and then transferred controls to the First Officer. The First Officer was flying and communicating with ATC whilst the Captain communicated with Maintenance Control; Dispatch and Flight Attendants. We continued our climb to 15000 for terrain avoidance and stayed in communication with ATC/Departure advising them of our current condition and that we will be returning to ZZZ after completing our checklists and communications with maintenance and our Dispatcher.The Captain assisted by the jump seater started the QRH procedure for loss of electrical stab trim. We ended up climbing to FL210 as our communications became scratchy with Maintenance Control. The speed trim fail light did not stay on the entirety off the flight. We complied with the stabilizer trim inoperative QRH procedure and diverted back to ZZZ. During our communication with ATC we [requested handling priority] with our electrical trim failure and had the personnel on standby for our landing. We transferred controls back; the Captain (CA) started the descent to ZZZ as we were cleared and told to expect ILS to Runway XXL. The First Officer (FO); assisted by the jump seater completed the final items in the QRH and the CA landed the aircraft. After landing we continued to taxi clear of the runway to our assigned gate and made all the ELB entries for the speed trim light; electrical stab trim inoperative and overweight landing.