The draft Trade and Cooperation Agreement between the EU and the UK has been published. Please find it attached. At first sight, it does not seem to contain any express provisions on civil justice by contrast with criminal justice. Subject to a more thorough reading, and the publication of any separate agreement (like the one on Security of Information or the one on Civil Nuclear), the silence seems deliberate. The presentation of the deal on the UK side seems to confirm this (see https://www.gov.uk/government/publications/agreements-reached-between-the-united-kingdom-of-great-britain-and-northern-ireland-and-the-european-union).
However, one should not forget the following:
“The Withdrawal Agreement remains in place […] the Withdrawal Agreement – and the Protocol on Ireland and Northern Ireland, in particular – will be implemented on 1 January. On 17 December, the EU-UK Joint Committee met to endorse all formal decisions and other practical solutions related to the implementation of the Withdrawal Agreement. As part of these mutually agreed solutions, the UK has agreed to withdraw the contentious clauses of the UK Internal Market Bill, and will not introduce any similar provisions in the Taxation Bill” (source: https://ec.europa.eu/commission/presscorner/detail/en/IP_20_2531). This sheds some lights in respect of some European Civil Justice / Private International Law instruments, albeit not all.