The phrase "study at contract" can be replaced with various synonyms, depending on the context in which it is being used. Some alternatives include "learn by agreement," "research through arrangement," "investigate under terms," and "examine based on a deal." These synonyms convey the idea that studying or researching is being done in a structured or contractual manner, with specific terms and conditions to be followed. It may relate to a research project, a business arrangement, or an academic study program. By using synonyms creatively, writers can add variety and nuance to their writing, making it more engaging and interesting to readers.