Hi,
There is no transfer of social security contributions from one country to another.
Your UK National Insurance account will only ever show the contributions that you’ve paid in the United Kingdom.
It is possible, however, that the contributions that you’ve paid in the Republic of Ireland may help with your UK Pension entitlement.
This is a question for The Pension Service, but at the time you make your claim to a UK Pension you would inform them that you had been in other countries
and they would do their calculations.
It would be of benefit to speak with The Pension Service, I note that you have tried to contact them but their contact details can be found here:-
Contact the Future Pension Centre
Thank you.