"第一期的" can be translated into English as "of the first phase" or "for the first installment/issue", depending on the context.
If referring to a project, program, or construction divided into phases, "of the first phase" is appropriate. For example, "the facilities of the first phase"(第一期的设施).
If referring to a series of publications, payments, or events divided into installments or issues, "for the first installment/issue" is suitable. For example, "content for the first issue"(第一期的内容) or "payment for the first installment"(第一期的款项).