It says he should wait a little, the time it takes for him to walk 8 feet, so he can have yishuv haddas so he can arrange his tefilos.
If that time has passed around 8-10 seconds, he can start with the Bal Tefilah, He doesn’t have to wait. Although he would miss Modim D’rabanan. He can say that in a different minyan. Its his choice, though I suggest the former as It might be considered a hefsek if he waits till after davening to make an hashlamah.
He does not have to be mechadesh anything(an additional request) in his tefillah, if he was an Oneis, as this is called a tefilas “Hashlama.”
Only if it is a tefillas Nedavah then one must add a new prayer.
Tefilas Hashlama can be done in the immediate following Shemoneh Esrei Of Shacharis Mincha and Maariv. If two prayers have passed he can only fix the latter one.
If he missed Shacharis and Mincha, he can daven at maariv two Shmoneh Esreis the first for maariv the second for Mincha, and he has lost the opportunity to redo Shacharis.
But He can do a Tefilas Nedava and in that he must be Mechadesh,
create a new personal prayer not included in the Shomneh Esrei.
I strongly remind one that when davening a Tefilas Nedavah,
one should make sure to concentrate the entire prayer as to what they are saying as this is a Nedava, and it will have an opposite
affect if one come to pray a nedavah and doesnt concentrate.
An Hashlama is something you can correct in the next prayer service if you were an Oneis (unable due unavoidable circustances not being your choice.) It’s not easy to define clearly.
A Nedavah is a prayer one wishes to give of his own accord just because. Not necessarily having to do with missing any prayer.
A Nedevah Requires that one should add a personal prayer, a chiddush, in addition ro what one normally says.
I believe a Meizid cannot daven a tefillas Hashlamah.
He can later pray a tefilas Neddava.
though I suggest one looks this up before they act.