Thank you for your question. There is not an "OPC position" on this question as such. That's the short and easy answer!
There have been a couple of GA study committees over the years that have produced reports that have some relevance to this question. You will find them at the bottom of this page: General Assembly Papers. The last two papers address "Women in Office" and two up from them is a report on "Unordained Persons in Worship." Note the status of such reports: weighty treatises but not part of the Constitution, which is the Bible, the Westminster Standards, and the Book of Church Order.
The reason that I say "some relevance" is because what you reference is prayer meeting, not a worship service, the primary focus of the study committee reports. There are varying views on this, though I think that a book like Noel Week's Sufficiency of Scripture (Banner of Truth) deals well with this sort of question both from the stance of principles and implementation (treating the key texts).
While I believe that 1 Timothy 2, 1 Corinthians 14, and other passages would teach that a women should not officially and publicly teach men or lead in any way in public worship, there is no clear biblical teaching that I see that would forbid a woman from praying in a prayer meeting. Those praying in such settings are neither leading nor teaching. If one thinks that those praying in such venues are leading or teaching, then we'd better not have them.
That having been said—that women may pray in a prayer meeting—that is not to say that women must pray in such settings. My wife never does nor ever would. She is not comfortable praying aloud in such settings and women must never be urged to do this against their wills. My wife prays in our and our family's prayers as well as in women's prayer time. So she does pray aloud with others, but not with men present (other than family members). That is her conviction. This does not mean, however, that women may not pray in such settings.
I trust that this is helpful for you.
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