If she has only the one source of income, she can only claim tax relief on her Civil Service superannuation contributions, but it's legal for her to make contributions to both. I'm assuming that the private one is a Personal Pension.
However, it would be more tax-efficient for her to cease contributions to the Personal Pension and look at buying back years in the superannuation scheme or making Addtional Voluntary Contributions (AVCs) with the money, as she can claim tax relief on such contributions.