The phrase "accept a relationship" is correct and usable in written English.
It can be used when discussing the willingness to embrace or acknowledge a romantic or interpersonal connection with someone.
Example: "After much contemplation, I finally decided to accept a relationship with him, realizing that we shared a deep bond."
Alternatives: "embrace a relationship" or "acknowledge a relationship".
He said Russia would never accept a relationship on those terms.
She would rather live alone than accept a relationship that compromises her independence.
He loves Ana and is willing to accept a relationship with her on her own terms: it will be "a vanilla relationship".
Jackson, whom Franklin describes as having been primed by her mother's criticisms "to accept a relationship with a man who treated her disrespectfully and shamed her for legitimate and rational desires," reluctantly went along with his terms.
That is the suggestion of James C. Dobson, one of America's leading evangelicals, who said Mr. Trump had recently come "to accept a relationship with Christ" and was now "a baby Christian".
In moments like this, it's clear that the inner circle of fans find Mr. Jackson's presence so exhilarating that they are willing to accept a relationship that is less than intimate at the center of their lives, because of the sense of adventure that it provides.
Whether considered one or two families, all past and present classifications accept a relationships between Cynomorium and Balanophoraceae.
The community in turn was no longer the lineal descent group with a parochial ritual tradition but the assembly (ekklēsia) of those who had through the covenant accepted a relationship to the dominion of Christ.
It is only the emergence of mass media in the last century that caused us to accept a passive relationship with culture.
I asked Natalie if she really thought the audience would accept a budding relationship between a 10 year old girl and the handsome adventurous Jesse.
"I think a modern Confucian perspective could accept a gay relationship if it was committed and constructive of lasting family bonds," Crane wrote on his blog The Useless Tree.
