It's not necessarily a contradiction. (By the way, the question the way you have put it has to do with logic and the philosophy of language and has nothing to do with psychology.) Before we begin, let's take a look at what definitons of the words "trust" and "anxiety" Merriam-Webster gives:
Trust - belief that someone or something is reliable, good, honest, effective, etc.
Anxiety - fear or nervousness about what might happen
Now, here's the catch: trust is something you have to a certain degree, but anxiety is something you either have or you don't. In other words, predicate like "I trust in X" "belongs" to the fuzzy logic, while the predicate "I have anxiety because I don't know if X will fail me or not" "belongs" to both the fuzzy logic and classical logic. It is surely a contradiction to say "I trust X completely and have anxiety because I don't know if X will fail me or not" , but it's not a contradiction to say "I trust X a little bit and have anxiety because I don't know if X will fail me or not". Taking this all into consideration, we can understand now why you even have this question: you speak English, and English (like virtually all natural languages) is vague. You cannot know for sure whether a person claiming "I trust X" really means "My level of trust in X is 100%" (i.e. "I trust X completely"), or if she really means "My level of trust in X is 99%" (can be obviously any number reasonably close to 100). So, in short the answer is that the statement "I trust X and have anxiety because I don't know if X will fail me or not" is a contradiction if and only if by "I trust X" the person claiming this really means "I trust X 100%". In all other cases, it is not technically a contradiction.