I am reasonably sure that the ROYAL IRISH RANGERS white on piper green embroidered cloth shoulder title was/is only worn on a brassard by some Army Cadet Force detachments in Northern Ireland.
Bear in mind that the Royal Irish Rangers were formed in 1968 (post Battle Dress so no need for cloth titles) and amalgamated with the Ulster Defence Regiment in 1992 to form the Royal Irish Regiment. There are plenty of pictures of 1 R IRISH during the first Gulf War (1991) and no evidence of cloth titles being worn with desert dpm uniform.
The shamrock badge is harder to explain, it looks 'home made' but is similar to the current TRF. The other possibility for the brassard is that it related to 4/5 RANGERS (V) the TA Battalion in Northern Ireland that is now 2 R IRISH of the Army reserve.
There seem to be a few Forum Members with NI local knowledge who may be more able to resolve this mystery.
Tim
The regimental shop sells a wide range of badges and insignia relating to the Royal Irish Regiment and its antecedants
https://www.royal-irish.com/shop