Monarch is popular within unit of measurement (4)
I believe the answer is:
king
'monarch' is the definition.
(I know that monarch can be written as king)
'popular within unit of measurement' is the wordplay.
'popular' becomes 'in' ('in' can mean trendy).
'within' means one lot of letters goes inside another.
'unit of measurement' becomes 'kg' (kg is a kind of unit of measurement).
'in' going within 'kg' is 'KING'.
'is' acts as a link.
(Other definitions for king that I've seen before include "One on throne" , "In Christianity, God or Jesus Christ" , "and 21 Across: Shakespeare play" , "Recipient of 10 21 [VELODROME GOLD]" , "Most important chesspiece" .)