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Suppose there is the following mapping with Edge NGram Tokenizer:

 "settings": 
 "analysis": 
 "analyzer": 
 "autocomplete_analyzer": 
 "tokenizer": "autocomplete_tokenizer",
 "filter": [
 "standard"
 ]
 ,
 "autocomplete_search": 
 "tokenizer": "whitespace"
 
 ,
 "tokenizer": 
 "autocomplete_tokenizer": 
 "type": "edge_ngram",
 "min_gram": 1,
 "max_gram": 10,
 "token_chars": [
 "letter",
 "symbol"
 ]
 
 
 
 ,
 "mappings": 
 "tag": 
 "properties": 
 "id": 
 "type": "long"
 ,
 "name": 
 "type": "text",
 "analyzer": "autocomplete_analyzer",
 "search_analyzer": "autocomplete_search"
 
 
 
 

And the following documents are indexed:

POST /tag/tag/_bulk
"index":
"name" : "HITS FIND SOME"
"index":
"name" : "TRENDING HI"
"index":
"name" : "HITS OTHER"

Then searching

 "query": 
 "match": 
 "name": 
 "query": "HI"
 
 
 

yields all with the same score, or TRENDING - HI with a score higher than one of the others.

How can it be configured, to show with a higher score the entries that actually start with the searcher n-gram? In this case, HITS FIND SOME and HITS OTHER to have a higher score than TRENDING HI; at the same time TRENDING HI should be in the results.

Highlighter is also used, so the given solution shouldn't mess it up.

The highlighter used in query is:

 "highlight": 
 "pre_tags": [
 "<"
 ],
 "post_tags": [
 ">"
 ],
 "fields": 
 "name": 
 
 

Using this with match_phrase_prefix messes up the highlighting, yielding <H><I><T><S> FIND SOME when searching only for H.

You must understand how elasticsearch/lucene analyzes your data and calculate the search score.

1. Analyze API

https://www.elastic.co/guide/en/elasticsearch/reference/current/_testing_analyzers.html this will show you what elasticsearch will store, in your case:

T / TR / TRE /.... TRENDING / / H / HI

2. Score

https://www.elastic.co/guide/en/elasticsearch/reference/current/query-dsl-bool-query.html

The bool query is often used to build complex query where you need a particular use case. Use must to filter document, then should to score. A common use case is to use different analyzers on a same field (by using the keyword fields in the mapping, you can analyze a same field differently).

3. dont mess highlight

According the doc: https://www.elastic.co/guide/en/elasticsearch/reference/current/search-request-highlighting.html#specify-highlight-query

You can add an extra query:

 "query": 
 "bool": 
 "must" : [
 
 "match": 
 "name": "HI"
 
 
 ],
 "should": [
 
 "prefix": 
 "name": "HI"
 
 
 ]
 
 ,
 "highlight": 
 "pre_tags": [
 "<"
 ],
 "post_tags": [
 ">"
 ],
 "fields": 
 "name": 
 "highlight_query": 
 "match": 
 "name": "HI"
 
 
 
 
 

In this particular case you could add a match_phrase_prefix term to your query, which does prefix match on the last term in the text:

 "query": 
 "bool": 
 "should": [
 
 "match": 
 "name": "HI"
 
 ,
 
 "match_phrase_prefix": 
 "name": "HI"
 
 
 ]
 
 

The match term will match on all three results, but the match_phrase_prefix won't match on TRENDING HI. As a result, you'll get all three items in the results, but TRENDING HI will appear with a lower score.

Quoting the docs:

The match_phrase_prefix query is a poor-man’s autocomplete[...] For better solutions for search-as-you-type see the completion suggester and Index-Time Search-as-You-Type.

On a side note, if you're introducing that bool query, you'll probably want to look at the minimum_should_match option, depending on the results you want.