Old dears discontented with betting shop offerings (4)
I believe the answer is:
odds
'shop offerings' is the definition.
The definition suggests a plural noun which matches the answer.
'old dears discontented with betting' is the wordplay.
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'discontented' means to remove the middle letters (the word's contents are removed).
'with' means one lot of letters go next to another.
'betting' becomes 'd' (I am not sure about this - if you are sure you should believe this answer much more).
'dears' with its centre taken out is 'ds'.
'ds' after 'd' is 'dds'.
'o'+'dds'='ODDS'
Can you help me to learn more?
(Other definitions for odds that I've seen before include "familiar to our betters?" , "The chances of something happening" , "prices" , "Chances expressed as a ratio" , "Things not even" .)