Is my common-law partner entitled to my defined contribution pension?

Not automatically; no. In contrast to legally-married partners (who are subject to different rules), if you were part of a common-law relationship that has ended, then your Ex is not automatically entitled to share in the value of your defined contribution pension.

Unless you and your Ex have an agreement stating otherwise, or else you have obtained a court order or an award made by an arbitrator directing your pension is to be shared (which will arise only rarely), then you are entitled to keep the full value of your pension in the event you and your partner split up.