... chasing King’s lost drawing (7)
I believe the answer is:
tracing
'drawing' is the definition.
(tracing is a kind of drawing)
'chasing king's lost' is the wordplay.
'chasing' becomes 'tracking' ('track' can be a synonym of 'chase').
'king' becomes 'K' (abbreviation for king in chess).
'lost' indicates named letters should be taken away.
'tracking' with 'k' removed is 'TRACING'.
(Other definitions for tracing that I've seen before include "Finding by investigation" , "produce copy?" , "Tracking or outlining on transparent paper" , "Hunting down" , "design" .)