It precedes fast run in dip by one tot heading west (5,4)
I believe the answer is:
mardi gras
'it precedes fast' is the definition.
(Lent is a fast after Mardi Gras or Shrove Tuesday)
'run in dip by one tot heading west' is the wordplay.
'run in dip' becomes 'gras' (I can't explain this - if you can you should believe this answer much more).
'by' means one lot of letters go next to another.
'one' becomes 'i' (Roman numeral).
'tot' becomes 'dram' (both can mean an alcoholic drink).
'heading west' shows that the letters should be reversed in order.
'i'+'dram'='idram'
'idram' backwards is 'mardi'.
'gras' after 'mardi' is 'MARDI GRAS'.
(Other definitions for mardi gras that I've seen before include "Shrove Tuesday festival" , "The lead up to fast" , "Time for carnival" , "pre-Lent festival" , "festive occasion" .)