No weaver bird, but a towel maker (5)
I believe the answer is:
owlet
'no weaver bird' is the definition.
'owlet' can be an answer for 'bird' (owlet is a kind of bird). I'm unsure of the 'no weaver' bit.
'a towel maker' is the wordplay.
'maker' indicates anagramming the letters (can make this from the letters).
'towel' with letters rearranged gives 'OWLET'.
'but' acts as a link.
Can you help me to learn more?
(Other definitions for owlet that I've seen before include "Young hooter" , "Towel (anag)" , "Young fly-by-night" , "Young nocturnal bird of prey" , "new hooter?" .)