The existence of compact leaves of codimension 1 foliations defined on 3-manifolds is characterized by Novikov see:
https://en.wikipedia.org/wiki/Novikov%27s_compact_leaf_theorem
If you read Novikov paper: (Theorem 6.1) and (Theorem 7.1) impliesimply that if the image of $t(A)\rightarrow \pi_1(M)$ has a non trivial kernel, then the foliation has a compact leaf, here $t(A)$ is the semi-group of homotopy class of tranversal through a point $x$ the leaf $A$. In particular, for a taut foliation one can define the class of the closed transversal in $t(A)$ for any leaf and apply the previous theorems if this class is a non trivial element of the kernel $t(A)\rightarrow \pi_1(M)$.