The correct phrase that appropriately completes the sentence is 'Has been teaching'.
'Has been' is used in the present perfect tense. The present perfect tense refers to an action that began at some time in the past and is still in progress.

The speaker is detailing an activity that happened in the past and is still in progress with the inclusion of the preposition 'since' in the sentence. We use since as a preposition with a date, a time, or a noun phrase as included in the statement.

If the question had read as; Mrs. Okoro .... in this school in 1975.
Then the correct option would have been 'taught'. That is,  'Mrs. Okoro taught in this school in 1975', (indicating that the activity had happened only in the past).

Therefore the preposition 'since' as used by the speaker in the statement indicates that, the activity happened in the past and is still in progress. Hence the statement would read;

Mrs. Okoro has been teaching in this school since 1975.