Tight trousers splitting finally, vehicle held overhead β strain every sinew (4,1,3)
I believe the answer is:
bust a gut
'strain every sinew' is the definition.
(to bust a gut is to work one's body very hard)
'tight trousers splitting finally vehicle held overhead' is the wordplay.
'tight' becomes 'taut' (synonyms).
'trousers' indicates putting letters inside (to trouser can mean to steal or take).
'finally' indicates one should take the final letters.
'vehicle' becomes 'bus' (bus is a kind of vehicle).
'held overhead' means one lot of letters go next to another (in a down clue, some letters go above others).
The last letter of 'splitting' is 'g'.
'taut' placed around 'g' is 'tagut'.
'tagut' put after 'bus' is 'BUST A GUT'.
(Other definitions for bust a gut that I've seen before include "Give it everything" , "Make a huge effort (slang)" , "Really work extra hard" , "Strain" , "Make a strenuous effort" .)