Notice redhead inside is nimble? (4)
I believe the answer is:
spry
'is nimble?' is the definition.
(synonyms)
'notice redhead inside' is the wordplay.
'notice' becomes 'spy' (spy can mean to notice or observe).
'redhead' becomes 'r' (head letter of 'red').
'inside' indicates putting letters inside.
'spy' enclosing 'r' is 'SPRY'.
(Other definitions for spry that I've seen before include "Far from doddering" , "Moving quickly and lightly" , "Nimble, brisk" , "Agile (for one's age?)" , "Energetic" .)