Slackened, becoming loose in a rush (7)
I believe the answer is:
relaxed
'slackened' is the definition.
(I've seen this before)
'loose in a rush' is the wordplay.
'loose' becomes 'lax' ('lax' is associated in meaning with 'loose').
'in' means one lot of letters goes inside another.
'a rush' becomes 'reed' (I've seen this before).
'lax' placed into 'reed' is 'RELAXED'.
'becoming' is the link.
(Other definitions for relaxed that I've seen before include "Without tension" , "Rested" , "Easy-going" , "Made (a rule) less strict" , "Having put one's feet up" .)