Measure cost supporting bird (7)
I believe the answer is:
titrate
'measure' is the definition.
(titrating is a kind of measuring)
'cost supporting bird' is the wordplay.
'cost' becomes 'rate' (rate is a kind of cost**).
'supporting' says to put letters next to each other (in a down clue, some letters go below others).
'bird' becomes 'tit' (I've seen this before).
'rate' put after 'tit' is 'TITRATE'.
(Other definitions for titrate that I've seen before include "Use indicator maybe" , "measure volume" , "Determine strength of solution (chem.)" , "Measure the strength of (a solution) using a reagent" , "Carry out scientific analysis" .)