Commercial Fixed Wing
Flight Crew Air Transport Pilot (ATP); Flight Crew Multiengine; Flight Crew Instrument
Flight Crew Last 90 Days 99; Flight Crew Total 6175; Flight Crew Type 6175
Human-Machine Interface; Situational Awareness
Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance
Air Traffic Control Issued New Clearance; Flight Crew Became Reoriented
Human Factors; Environment - Non Weather Related
We were on a left downwind for [Runway] XXC at ZZZ at 4;000 feet.  The Captain; who has only flown 1 trip since February 2020 (and done 1 [training] event); was the pilot flying.  It was at the end of a ZZZ1 - ZZZ all-nighter.  Approach Control assigned us to turn left to heading 360.  I acknowledged the heading assignment while the Captain entered the heading in the MCP and pushed HDG SEL which I watched him do.  A few seconds later I realized that we had not started turning; so I pointed that out to the Captain who re-pushed HDG SEL.  We both verified the FMA and the airplane started its turn.  A few seconds later Approach called; said something about being behind the turn and gave us farther left to heading 310 which I acknowledged and the Captain dialed in.  Then a few seconds later Approach called again and asked if there was something wrong with the initial heading assignment of 360 and he mentioned that we went 3 - 4 miles before actually starting our turn for 360.  I answered: 'No; we dialed it in; pushed for heading but it didn't take and it just took us a few seconds to realize it.'  The Controller responded with 'OK' and the rest of the flight went uneventfully.
Final Approach Controller gave us a left turn to 350. I put 350 in the window and pushed heading select. I looked to the left to see if the airport was in sight. I did not verify the FMA. After 10-15 seconds my First Officer said; you're not turning. Immediately reselected heading select; VERIFIED the FMA and verified turn.
Air carrier flight crew reported the aircraft did not start the turn as expected because they had not activated heading select.