"My manager agreed to let me get promoted."
I agree. This "让" has a more active sense.
We could even translate the phrase as "agreed to promote me".
I have learned that 的 may only be omitted for close familial relations.
I guess you can ask what it means to say "My manager agrees to let me get promoted". Typically, if he (or she) agrees, then he has agreed, i.e. he has signaled his agreement by explicitly agreeing at some past time, i.e. he agreed at that time, and presumably his agreement still stands.
I think there can be a "了" in this sentence, but there doesn't need to be, and without it, the sentence can be translated into the past tense or the present tense.