Showing signs of age is bound to inspire resistance (5)
I believe the answer is:
tired
'showing signs of age' is the definition.
(tired can old or weary)
'bound to inspire resistance' is the wordplay.
'bound' becomes 'tied' ('tie' can be a synonym of 'bind').
'to inspire' indicates putting letters inside (breathe in).
'resistance' becomes 'r' (electronics abbreviation).
'tied' placed around 'r' is 'TIRED'.
'is' acts as a link.
(Other definitions for tired that I've seen before include "Dressed once" , "getting bored" , "Ready to drop" , "Sleepy" , "Are American cars so" .)