Fat Australian vice-regal inside is a slowcoach (7)
I believe the answer is:
laggard
'a slowcoach' is the definition.
(I've seen this before)
'fat australian vice-regal inside' is the wordplay.
'fat' becomes 'lard' (lard is a kind of fat).
'australian' becomes 'A' (common abbreviation).
'vice-regal' becomes 'gg' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'inside' is an insertion indicator.
'a'+'gg'='agg'
'lard' enclosing 'agg' is 'LAGGARD'.
'is' is the link.
Can you help me to learn more?
(Other definitions for laggard that I've seen before include "Loiterer" , "one going slowly" , "who's getting behind?" , "Dawdler" , "Drag gal around for one who falls behind" .)