time of year vs time period

time of year and time period both are nouns.

Word	Noun	Adjective	Verb	Adverb
time of year	Yes	No	No	No
time period	Yes	No	No	No

As nouns, time period is a hypernym of time of year; that is, time period is a word with a broader meaning than time of year:

time of year: one of the natural periods into which the year is divided by the equinoxes and solstices or atmospheric conditions
time period: an amount of time

Other hypernyms of time of year include period, period of time.

time of year (noun)	time period (noun)
one of the natural periods into which the year is divided by the equinoxes and solstices or atmospheric conditions	an amount of time