Dog taken to vet with no tail to bend (5)
I believe the answer is:
curve
'bend' is the definition.
(curving is a kind of bending)
'dog taken to vet with no tail' is the wordplay.
'dog' becomes 'cur' (cur is a kind of dog).
'taken to' is a charade indicator (letters next to each other).
'with no tail' means to remove the last letter.
'vet' with its last letter removed is 've'.
'cur'+'ve'='CURVE'
'to' is the link.
(Other definitions for curve that I've seen before include "Non-straight line" , "Wind" , "No part of this line is straight" , "Line on a graph" , "Not the straightforward" .)