Like some fat Tudor composer keeping old wife and horse (9)

'like some fat' is the definition.
(tallow is a type of animal fat)

'tudor composer keeping old wife and horse' is the wordplay.
'tudor composer' becomes 'tallis' (choral composer Thomas Tallis).
'keeping' indicates putting letters inside.
'old wife' becomes 'ow' (this might be a standard abbreviation of which I'm unaware).
'and' means one lot of letters go next to another.
'horse' becomes 'h' (synonyms).
'tallis' enclosing 'ow' is 'tallowis'.
'tallowis'+'h'='TALLOWISH'