Refers to someone new to a field or activity, often with a nuance of inexperience or being a fledgling. The term 駆け出し itself means 'starting out' or 'running out', and adding 者 makes it a person.
He's still a beginner, but he's full of motivation.
駆け出し者の私には、この仕事は荷が重い。
This job is too much for a novice like me.
初心者 is the most common and neutral word for 'beginner'. 駆け出し者 carries a nuance of someone who has just started and is still inexperienced, often in a professional or skill-based context.
新米 also means 'novice' or 'newcomer', but is often used in workplace or organizational settings. 駆け出し者 is more about being at the start of one's career or pursuit.
Compound of 駆け出し (kakedashi, 'starting out, novice') + 者 (mono, 'person'). 駆け出し is the nominalized form of the verb 駆け出す (kakedasu, 'to run out, to dash out'), metaphorically referring to someone who has just started running (i.e., their career or endeavor).