Many clients ask for exercises they can do between sessions. Experiencing and embodying compassion is an importat feature of the therapy and I always encourage my clients to work some form of self-practice between the sessions. It can look very differently but I was myself helped, in my self-practise, by having audio meditations I could follow. My mind tends to wander off very easily and unless I keep it tethered by either a yoga position and someone's voice I find it hard to stay with the practise.
The Compassionate Mind Foundation in the UK has released a number of different meditiative practises tailored towards working with Compassion. I warmly recommend you to try them and just notice what happens. What comes up? Sometimes it is not what we expect, sometimes it can help us get in touch with blocks and fear. So keep an open mind and just allow what comes to come.