In the 21st century globalization accelerates the need for English communication skills as English is recognized as a lingua franca in the business world. A high priority of university educators involved in LSP (LSP – language for special purposes) training is to equip graduates with communicative LSP skills meeting the standards of huge and increasingly competitive job market. The study addresses the issue on how to close the current gap between prospective employers’ expectations of English communication skills level and the existing LSP level of graduates. The study aims at, first, to reveal the effect of English globalization on employability from the perspective of university students; second, to identify factors leading to reticence in speaking; and third, to provide a solution to the problem of gap between graduates’ oral skills and employers’ expectations. The study uses two questionnaires as an instrument to collect data. The obtained quantitative data is used as an input for qualitative study. The study certifies that undergraduates are fully aware of the utmost importance of English language for employment. Also, the study identifies the main social and psycholinguistic reasons hindering to develop speaking skills in the university settings. Further, the research findings have been used to develop and integrate into university training curricula an intensive 3-module program meeting the real needs of students and business community. The goal of this program is to equip students with excellent English communication skills meeting the rapidly changing job market demands. The findings of the study suggest that LSP training offered at higher school should be improved to meet job market requirements. The study enabled to assess the instruction results and provide a solution to the problem of “competency gap”. It points to where the real work of closing the gap between the need for workforce skilled in English communication and actual graduates’ skill level needs to happen.