Entity Linking (EL) maps an entity mention in a natural language sentence to an entity in a knowledge base (KB). The Zero-shot Entity Linking (ZEL) extends the scope of EL to unseen entities at the test time without requiring new labeled data. BLINK (Wu et al., 2020) (BERT-based) is one of the SOTA models for ZEL. Interestingly, we discovered that BLINK exhibits diminishing returns, i.e., it reaches 98% of its performance with just 1% of the training data and the remaining 99% of the data yields only a marginal increase of 2% in the performance. While this extra 2% gain makes a huge difference for downstream tasks, training BLINK on large amounts of data is very resource-intensive and impractical. In this paper, we propose a neuro-symbolic, multi-task learning approach to bridge this gap. Our approach boosts the BLINK's performance with much less data by exploiting an auxiliary information about entity types. Specifically, we train our model on two tasks simultaneously - entity linking (primary task) and hierarchical entity type prediction (auxiliary task). The auxiliary task exploits the hierarchical structure of entity types. Our approach achieves superior performance on ZEL task with significantly less training data. On four different benchmark datasets, we show that our approach achieves significantly higher performance than SOTA models when they are trained with just 0.01%, 0.1%, or 1% of the original training data. Our code is available at https://github.com/IBM/NeSLET.