Lively old air, inspiring finale of Beethoven's ninth? (7)
I believe the answer is:
ordinal
'ninth?' is the definition.
(similar in meaning)
'lively old air inspiring finale of beethoven's' is the wordplay.
'lively' is an anagram indicator (I've seen this in other clues).
'inspiring' means one lot of letters goes inside another.
'finale of' says to take the final letters.
The final letter of 'beethoven' is 'n'.
'old'+'air'='oldair'
'oldair' is an anagram of 'ordial'.
'ordial' going around 'n' is 'ORDINAL'.
(Other definitions for ordinal that I've seen before include "Number defining a thing's position in series" , "Like "first" or "third"" , "E.g. first" , "Of position in series; service book (hist.)" , "First, second, third could be such a numeral" .)