We finally give thought to cutting dance for greater number (13)
I believe the answer is:
preponderance
'greater number' is the definition.
'preponderance' can be an answer for 'number' (preponderance is a kind of number). I am not certain of the 'greater' bit.
'we finally give thought to cutting dance for' is the wordplay.
'finally' indicates one should take the final letters.
'give thought to' becomes 'ponder' (I've seen this before).
'cutting' is an insertion indicator (some letters cut their way into a word).
'dance for' becomes 'prance' (I can't justify this - if you can you should believe this answer much more).
The final letter of 'we' is 'e'.
'e'+'ponder'='eponder'
'eponder' placed into 'prance' is 'PREPONDERANCE'.
(Other definitions for preponderance that I've seen before include "In majority of" , "Quality of outweighing other factors etc" , "Dominance" , "Superiority in numbers" , "Predominance" .)