Read the deed and 1. see if there is the power to add, then 2. see how has this power, then 3. have this person or person's exercise the power 4. record the decision in a deed. But first the trustee should get some legal advice on the stamp duty, taxation and other consequences.
Depends on the wording of the trust deed. For example, a deed may allow secondary benficiaries that aren't named at creation, but outline that future relationships can be added, such as unborn children, adopted or permanent care children, future spouses, etc, etc, etc. There's plenty of ways a trust deed could be worded for future beneficiaries, it depends on what you want. If the trust deed is still being set up, discuss with the solicitor writing the deed. If the deed has been created and you're unsure on what can be done, seek legal advice. There may also be the provision to change the deed.
Many discretionary trust deeds effectively have your extended family as the trust beneficiaries. So if the person is, or becomes a member of your family most discretionary trusts will allow this person to benefit from the trust just be electing to distribute income or capital. You should read the deed (of course) but the chances are that you are effectively there. If you change the primary beneficiaries you might create problems.
Instead of adding some you could marry then perhaps. Another way may be to set up a new trust and have one trust distribute to another. Or set up a company. But you must make sure the trust or company falls under the definition of beneficiary.
And consider if a family trust election is required (and may limit who the tax beneficiaries are) or even permits that person to be a beneficiary (not called a member). Tax issues occur if external beneficiaries are sometimes added