Spider spinning on banks of Rhine showed signs of life (8)

'showed signs of life' is the definition.
(to respire is to breathe)

'spider spinning on banks of rhine' is the wordplay.
'spinning' indicates an anagram.
'on' is an insertion indicator (as in clothing 'on' a person).
'banks of' means to remove the middle letters (the banks are the sides of the word).
'rhine' with its middle removed is 're'.
'spider' with letters rearranged gives 'respid'.
'respid' going around 're' is 'RESPIRED'.