Tied up to deter the straying (8)
I believe the answer is:
tethered
'tied up' is the definition.
(I've seen this before)
'deter the straying' is the wordplay.
'straying' is an anagram indicator.
'deter'+'the'='deterthe'
'deterthe' with letters rearranged gives 'TETHERED'.
'to' acts as a link.
(Other definitions for tethered that I've seen before include "Confined in range by tied rope" , "Of animal, with rope fastened to prevent straying" , "Tied to something with a rope" , "Of animal, secured or hobbled" , "Restrained with a rope" .)