Increase number slightly during collection (7)
I believe the answer is:
roundup
'collection' is the definition.
(I have seen 'Collection of facts ' mean 'roundup' so perhaps 'collection' could also mean 'roundup')
'increase number slightly during' is the wordplay.
I cannot really see how this works, but
'increase' could be 'up' (upping is a kind of increasing) and 'up' is found in the answer.
'number' could be 'round' (I have seen 'number of drinks' mean 'round' so perhaps 'number' could also mean 'round') and 'round' is present in the answer.
No letters remain.
This explanation may well be incorrect...
Can you help me to learn more?
(Other definitions for roundup that I've seen before include "Summary (of events)" , "Gather into one place, animals or people" , "Gathering of cattle or summary" , "Gather together" , "A systematic gathering" .)