Not a weaver bird, but a towel maker (5)
I believe the answer is:
owlet
'not a weaver bird' is the definition.
I can't tell whether this definition defines the answer.
'a towel maker' is the wordplay.
'maker' indicates an anagram (can make this from the letters).
'towel' with letters rearranged gives 'OWLET'.
'but' is the link.
Can you help me to learn more?
(Other definitions for owlet that I've seen before include "Wise young" , "Young bird; moth" , "Little nocturnal bird" , "One may give a little screech" , "Young fly-by-night" .)