Thin coil finally used in transmitter (7)
I believe the answer is:
slender
'thin' is the definition.
('slender' can be a synonym of 'thin')
'coil finally used in transmitter' is the wordplay.
'finally' suggests the final letters.
'used in' is an insertion indicator.
'transmitter' becomes 'sender' ('sender' can be a synonym of 'transmitter').
The last letter of 'coil' is 'l'.
'l' placed within 'sender' is 'SLENDER'.
(Other definitions for slender that I've seen before include "Slight, slim" , "with a narrow outlook" , "inadequate" , "Fine" , "Spare" .)