Dramatic Links beyond Leitmotifs
There are many more possibilities when scoring a film (or rather when writing music at all) to create dramatic connections. Every single musical element can serve the purpose of connecting cues.
Obviously, a melodic idea is the standard way to connect things, mainly coming from the leitmotif technique but also harmonic language can connect. Using the same chord progression or types of chords will create a rather unique quality that is great to link cues. But also, orchestration can be a strong factor. Using a specific solo instrument or a specific set of instruments to portray a situation or an emotion whenever it occurs will make connections between cues, even if the melodic and even harmonic ideas are different.
Even such a simple thing as a rhythm can be enough to link cues and situations. Think about the ticking of the Joker in THE DARK KNIGHT or the slightly dated sounding but still popular TERMINATOR 2 signature rhythm. Your score will in general feel more colourful and multilayered the more variety you use when choosing your linking elements. But as usual: overdoing is a danger here as well.