As codified in Shulchan Aruch (OC 19:1) the requirement to don tzitzit is an obligation on the individual, i.e. when one wears a garment which meets the requirements of the laws of tzitzit he is then obligated to attach the strings. One is not obligated to purchase a kosher garment bearing tzitzit in order to fulfill the commandment (cf. Beer Heitiv OC 17:2), however it is preferable to do so as it is of great significance (see SA ibid. 24:1; the rabbis have much discussion about the notion of proactively obligating oneself in mitzvot generally but that is off topic). This is the only biblical "obligation". Therefore, if one does not have a talit gadol or tzitzit while praying, and he prays without them, he may don them later in the day but is not halachically obligated to do so.
Tzitzit is tied to praying in certain areas of prayer and SA (ibid) therefore recommends the donning of tzitzit at least during prayers.
Since the donning of tzitzit and tefilin are not halachically bound together, if one has tzitzit by prayers but does not have tefilin they may pray with tzitzit alone. When they don the tefilin later (in order not to transgress the rabbinic dicutm (Ber. 14b) "one who reads the keriat shema without wearing tefilin is likened to offering false testimony") there is no halachic obligation to re-don the tzitzit. If the case is the opposite, one dons the tefilin without the tzitzit since, again, the two are not mutually conditional.
If one was wearing a talit katan all along, he has fulfilled the tzitzit commandment (cf. SA ibid 8:3) and is not at all obligated to don the talit gadol later in the event that he did not have it while praying or wearing tefilin and would like to don them together.
