Dog with a tail to shorten (7)
I believe the answer is:
curtail
'shorten' is the definition.
(I know that curtail is a more specific form of the action shorten)
'dog with a tail' is the wordplay.
'dog' becomes 'cur' (a cur is an aggressive or scruffy dog).
'with' means one lot of letters go next to another.
'cur'+'tail'='CURTAIL'
'to' is the link.
(Other definitions for curtail that I've seen before include "Reduce in length" , "Impose a restriction on" , "Abbreviate" , "'Cut short, restrict (7)'" , "Cut short (an activity)" .)