What dog may do to welcome garden visitor? (7)
I believe the answer is:
wagtail
'garden visitor?' is the definition.
(type of bird)
'what dog' is the wordplay.
'what' becomes 'wag' (I can't justify this - if you can you should believe this answer much more).
'dog' becomes 'tail' ('tail' can be a synonym of 'dog').
'wag'+'tail'='WAGTAIL'
'may do to welcome' is the link.
I am not very happy about this link. Some or all of it may be part of another bit of the clue.
(Other definitions for wagtail that I've seen before include "Songbird - gala wit (anag)" , "singer" , "Common bird" , "I tag law of the bird" , "Slender songbird - a law git (anag)" .)