The phrase "a second requirement of" is correct and usable in written English.
You can use it when discussing multiple criteria or conditions that need to be met in a particular context, such as in a report or an academic paper.
Example: "A second requirement of the project is to ensure that all data is collected within the specified timeframe."
Alternatives: "an additional requirement of" or "a further condition of".
We turn next to a second requirement of the Free Exercise Clause, the rule that laws burdening religious practice must be of general applicability.
A second requirement of the 2010 Healthy, Hunger-Free Kids Act also raises nutritional standards for food sold in schools but away from the lunch line — snacks and drinks in vending machines, school stores and fundraisers.
A second requirement of independent study in the chemistry department is the preparation and presentation of a poster describing your research.
A second requirement of our new strategy is that the effects of the new drugs or implementations should be transient.
A third requirement of due process is that all evidence be considered.
This consideration leads to a second requirement for comparative meta-analyses of diagnostic studies: the meta-analytic methods should adjust for the use of imperfect reference standards.
A first requirement for topographic mapping of a given area is an adequate pattern of horizontal and vertical control points, and an initial step is the assembly of all such existing information.
Thus, we suggest that a third requirement for tight coupling of the SecY-complex to the ribosome is an electrostatic interaction between the negatively charged rRNA of H59 and positively charged residues in a cytoplasmic domain of the nascent IMP.
> -wrap-foot> A second requirement is that the amount of preprocessing time needed to create the index data structures should be reasonable.
A second requirement is to have some means of separating the learning and the decision phases.
The second requirement of a good biography is vivid detail.
