He is seen as a strong candidate for the next company president.
The next president will take office next month.
The bill is scheduled to be debated in the next Diet session.
The next model is expected to come with new features.
来期 specifically means the next fiscal or academic year, whereas 次期 can refer to any upcoming term, political or organizational.
次代 suggests the next generation or era in a broader historical sense, while 次期 usually refers to a concrete upcoming term or version.
時期 (also read じき) means 'time' or 'season' in general, while 次期 specifically means 'the next term or version'; the identical reading makes them easy to mix up in speech.
Compound of 次 (next) and 期 (period, term).