こんなのがあった場合、

Model.scala

import play.api.db.DB
import play.api.Play.current
import scala.slick.driver.MySQLDriver.simple._
import scala.slick.jdbc._
import scala.language.postfixOps

case class Model(id:Int, name:String)

object Models extends Table[Model]("models") {

  def id      = column[Int]("id", O.PrimaryKey, O.AutoInc)
  def name = column[String]("name", O.NotNull, O DBType "varchar(100)")
  def * = id ~ name <> (Model.apply _, Model.unapply _)
  
  /** DBコネクション */
  val database = Database.forDataSource(DB.getDataSource())
 
  /** 登録 */
  def create(e: Model) = database.withTransaction { implicit session: Session =>
    Models.insert(e)
  }
}

Database.threadLocalSessionをimportするとimplicit ....がいらないらしい

Model.scala

import play.api.db.DB
import play.api.Play.current
import scala.slick.driver.MySQLDriver.simple._
import scala.slick.jdbc._
import Database.threadLocalSession
import scala.language.postfixOps

case class Model(id:Int, name:String)

object Models extends Table[Model]("models") {

  def id      = column[Int]("id", O.PrimaryKey, O.AutoInc)
  def name = column[String]("name", O.NotNull, O DBType "varchar(100)")
  def * = id ~ name <> (Model.apply _, Model.unapply _)
  
  /** DBコネクション */
  val database = Database.forDataSource(DB.getDataSource())
 
  /** 登録 */
  def create(e: Model) = database.withTransaction {
    Models.insert(e)
  }
}