Other work will include commissioning research into people’s experiences of accessing medical and clinical care.
Council leader Liz Leffman said any changes made would be “considered”.
The measures were initially agreed by the council in April after they were proposed by Liberal Democrat councillor Sally Povolotsky.
In total, 36 councillors voted in favour of the motion and 17 abstained with none against.
The plan, discussed at a meeting on Tuesday, will include ensuring the council’s services are “fully accessible, regardless of their sexuality or gender identity”.
The authority said it would also reduce the amount of gender information it collects and respect the pronouns people use to describe themselves.
“We want to carry out in-depth engagement so that we fully understand the thoughts and experiences of transgender and non-binary people in our communities,” Ms Leffman said.
“Once that information is gathered we can then begin to implement changes to council policies, in line with what the motion asked for.
“This is not going to be an overnight change, but is going to take the form of considered policy development informed by insight from our communities.”
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