Using unpublished data from previous supervisor for thesis I'm considering a change of my PhD supervisor due to strained relationship with my supervisor and changed of thesis direction (from practical to theoretical based on same topic). However, my thesis is heavily based on a set of data collected by a collaborator, but is given to me as my thesis project by my current supervisor. 

My question is, if I switched supervisor, would it be fine if I continue to use the data for my thesis? The data is unpublished, but I do not intend to use the data for any publication purpose. 

Any advice is much appreciated.
You ask: "would it be fine..", and I am inclined to ask back: fine by whom? There are several people involved, and it seems you are in a situation where you, no matter what you do, cannot make everybody happy. Therefore you need to decide who you want to make happy.

1) Your collaborator. If you have received data from a collaborator under pretense that it should be used for an article together with your old supervisor and said collaborator, it is unethical (and possibly violating some policy) to use that data for another purpose without having cleared it with this person. You need to contact your collaborator, explain the situation, and ask for permission. Remember that the data will be semi-public after thesis publication, given that the thesis is public.

2) Your new supervisor. It would be a poor start with your relationship with a new supervisor, if you pull a stunt he/she considers unethical. Discuss the situation with you new supervisor, for your future relationship's sake. On the other hand, if your new supervisor is counting on you to bring an almost-done thesis, only to find out that you have no data, that would also strain the relationship.

3) Your old supervisor. Is this going to burn a bridge you would rather leave un-burned. Are there even any bridges left? Make up your mind about that for yourself, unless your situation is vastly different from most supervisor switch situations, a discussion will not give you much.