As a Single Scheme member you can take out an AVC and get tax relief up to the Revenue limits for your age.
There are two ways of going about this. One is via the provider linked to your public sector employer (usually Cornmmarket:
https://www.cornmarket.ie/uploads/13292_AVC_Scheme_Member_SQ_Booklet_08-18_REBRANDED_FA_WEB.pdf). The advantage of this approach is convenience. Once you set up your AVC with your Cornmarket rep, your contributions are deducted at source in your wages' office and the tax relief applied there too. Administratively you can more or less forget about it.
The other option is to set up a PRSA-AVC with any of the other providers. I don't know the comparison but there have been several contributors on here saying that they got better value as regards charges and fees by going this route. The downside is that you have to pay your contributions directly from your taxed wages (direct debit) and claim the tax back from Revenue via your annual tax returns.
Keep in mind that with both of these options your benefits are linked to your main scheme. If you are short you can top up the tax free lump sum to the max allowed in your main scheme - the rest is usually transferred to an ARF. You cannot draw down any of these benefits until you retire, either at normal retirement age (68 if born after 1st Jan, 1961), via cost-neutral early retirement or, if it should transpire, ill-health retirement. In that regard, AVCs are more complementary to regular saving than a substitute.
This document from the Pensions Authority predates the Single Scheme but you may find the info on AVCs and PRSA-AVCs useful (I don't think PNS applies to the Single Scheme in the conventional sense described here) : [broken link removed]