Usually, pilots will check NOTAMs during pre-flight prep. Are there some situations where they use them in a specific flight phase? If yes, in which case would it be useful?
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Or, the classic, is that there are standing NOTAMs in the UK that overflying Ukraine and Syria aren't recommended. Not something most pilots need to worry about.
There is no expectation to check NOTAMs after departure, however.
NOTAMs are a planning aid. Before flight you look at the NOTAMs that are applicable to your route, including diversion airfields, and extrapolate the information you need. A NOTAM may make you change your route, or take a note to use a different frequency or procedure. You may make a notation on a map, for example, or a hand-written note on your pad, presuming you use one.
Once flying it's unlikely you'd refer to NOTAM text, they are terse and can be cryptic, and often require plotting on a map. You may bring a printout of frequency changes I suppose, but that would be the extent of it. Some navigation systems can use NOTAM data to enrich a moving map, which is handy as a visual reference.