Watch part of flight: people are on time (10)
I believe the answer is:
escapement
'watch part' is the definition.
'escapement' can be an answer for 'part' (I have seen 'part of watch' mean 'escapement' so perhaps 'part' could also mean 'escapement'). I'm not certain of the 'watch' bit.
'flight people are on time' is the wordplay.
'flight' becomes 'escape' (flight can mean an escape).
'people' becomes 'men' (men are people).
'are on' says to put letters next to each other (in a down clue, letters appear on others).
'time' becomes 't' (abbreviation).
'escape'+'men'+'t'='ESCAPEMENT'
'of' acts as a link.
Can you help me to learn more?
(Other definitions for escapement that I've seen before include "piano piece" , "Clock or watch mechanism" , "One-time flight" , "Part of watch mechanism" , "Part of A Clockwork" .)