If your partner does not have sufficient income to be liable to pay tax AND you only pay tax at the basic (20%) rate then it is possible for your partner to transfer part of their allowance to you. Unfortunately we cannot do this for you as your partner is the one who has to make the application, not the tax-payer.
This can be done online at https:www.gov.uk/marriage-allowance and you will need both your NI numbers and one of a range of different acceptable forms of ID for the non-taxpayer. If it is not possible to do this via the web then they can ring the tax office on 0300 200 3300. Please bear in mind that this transfer can only be done between couples who are married, or in a civil partnership.