High resolution spectroscopy, metrology and quantum technologies (e.g. trapping and cooling) require precision laser sources with narrow linewidth and wavelength tunability. The widespread use of these lasers will be promoted if they are cost-effective, compact and efficient. Alexandrite lasers with a broad tuning band pumped efficiently by low-cost red diodes are a potential candidate, but full performance as a precision light source has not been fully achieved. We present in this work the first continuous-wave (CW) and single-frequency operation of a unidirectional diode-end-pumped Alexandrite ring laser with wavelength tunability. An ultra-compact bow-tie ring cavity is developed with astigmatic compensation and a novel 'displaced mode' design producing CW output power > 1 W in excellent TEM00 mode (M2 < 1.2) when using a low brightness pump (M2 ≥ 30). Wavelength tuning from 727 - 792 nm is demonstrated using a birefringent filter plate. This successful operation opens the prospects of precision light source applications.