Thanks, Euterpe. That helps to clarify things. In fact, I'm going to change my mind about who or what is "pious and dutiful": it's Theodosia, not the city. The city has not been taking care of itself. Your latest text, τὴν ἔκ πολλῶν χρόνων ἔμελημένην καὶ πεπτωκυῖαν ἄγοραν ἐπιφανῶς κατασκευάσαι, ... means "[she pledged] splendidly to restore the agora, which had been neglected for many years and was in a state of collapse." And I learn from you that Theodosia was not a provincial ruler (or wife of a ruler), but a benevolent citizen of Arkesine who simply cared about her town, piously and dutifully.
As for Ἐπηγγείλατο, it's the aorist middle, third person singular, of ἐπαγγέλλω, "order, promise, profess."