Gill's brief period of rest? (8)
I believe the answer is:
breather
'rest?' is the definition.
(I know that breather is a type of rest)
'gill's brief period' is the wordplay.
I cannot quite understand how this works, but
'period' could be 'breath' (breath is a kind of period) and 'breath' is located in the answer.
The remaining letters 'er' is a valid word which might be clued in a way I don't understand.
This may be the basis of the clue (or it may be nonsense).
'of' acts as a link.
Can you help me to learn more?
(Other definitions for breather that I've seen before include "Informally a pause for rest - or to take in air" , "One who inspires" , "time off work" , "Short pause for rest" , "One's probably not dying" .)