Here is a relevant Wikipedia article: Nominal TAM
There is a fair amount of literature that mentions the existence of languages that mark tense on nouns; the first result I found on Google was this paper by Judith Tonhauser, "Towards an Understanding of the Meaning of Nominal Tense" (2005), about Paraguayan Guaraní. Depending on the language, the meaning of a past-tense-marked noun may be along the lines of “an ex-/former [noun]”. Here is Tonhauser's first set of illustrative examples:
(1) a. Kuehe a-hecha pa’i-pe.
yesterday I-see priest-PE
‘Yesterday I saw the priest.’
b. Kuehe a-hecha pa’i-kue-pe.
yesterday I-see priest-KUE-PE
‘Yesterday I saw the former priest.’
c. Kuehe a-hecha pa’i-rã-me.
yesterday I-see priest-RA-PE
‘Yesterday I saw the seminarist/future priest.’
Tonhauser actually argues that -kue and -rã mark nominal aspect, not tense (§1.1), although I would guess that, as with the English "perfect" construction, this is an area where different theorists may use different classifications. The similarity to English "temporal adjectives" such as former and future is mentioned in section 2 (p. 484); however, apparently there are some contexts where the Guarani constructions are not semantically equivalent to these English constructions.
There are also languages that use different “subject pronouns” for different tenses of the associated clause.
I don’t think it’s common for clausal tense to be marked on a non-pronominal noun in the clause. The Wikipedia article has a section "Clausal nominal TAM" where it mentions marking clause TAM on subject pronouns, definite articles, or though different kinds of case-marking.