。
Tests start next week.
Literal
Next-week from tests [subject-が] begin.
A simple temporal-source statement: ~から ('from / starting from') + subject + 始まる ('begin'). 始まる is the intransitive 'begin / start happening,' paired with the transitive 始める ('start [something]'). The casual だ copula is dropped — common in headline-like or schedule-like statements.