Good luck, but carving a PST file is very unlikely to work.
My reasons are that PSTs tend to be large. PSTs tend to grow. Both of these reasons mean that there is a very high chance that the PST will be fragmented. Straight carving will not recover fragments - it requires extra intelligence to find potential fragments and stitch them back.
Your best hope - for a NTFS disk is to see if you can find the relevant associated MFT entry for the file.
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