Knowledge Hypergraphs, as the generalization of knowledge graphs, have attracted increasingly widespread attention due to their friendly compatibility with real-world facts. However, link prediction in knowledge hypergraph is still an underexplored field despite the ubiquity of n-ary facts in the real world. Several recent representative embedding-based knowledge hypergraph link prediction methods have proven to be effective in a series of benchmarks, however, they only consider the position (or role) information, ignoring the neighborhood structure among entities and rich semantic information within each fact. To this end, we propose a model named EnhancE for effective link prediction in knowledge hypergraphs. On the one hand, a more expressive entity representation is obtained with both position and neighborhood information added to the initial embedding. On the other hand, rich semantic information of the involved entities within each tuple is incorporated into relation embedding for enhanced representation. Extensive experimental results over real datasets of both knowledge hypergraph and knowledge graph demonstrate the excellent performance of EnhancE compared with a variety of state-of-the-art baselines.