Recalled cunning corporation chasing Swindon's foremost rock band (7)
I believe the answer is:
stratum
'rock band' is the definition.
(I've seen this before)
'recalled cunning corporation chasing swindon's foremost' is the wordplay.
'recalled' is a reversal indicator (to recall can mean to bring something back).
'cunning' becomes 'art' (both can mean artfulness or trickery).
'corporation' becomes 'tum' ('corporation' can humorously mean belly fat).
'chasing' says to put letters next to each other (some letters chase after others).
'foremost' indicates taking the first letters.
The first letter of 'swindon' is 's'.
'art' back-to-front is 'tra'.
'tra'+'tum'='tratum'
'tratum' after 's' is 'STRATUM'.
(Other definitions for stratum that I've seen before include "(Geological) layer" , "Layer (of rock)" , "rock band" , "Social class - level" , "stretch of rock" .)